The first electron in both the cases has to "be removed from 3s-orbtials, but nuclear charge of Na is less than that of Mg. Hence I.E. of Na is lower them that of Mg.After the loss of first electron the electronic con-figuration of ${{Na}^{+}}$ is1${{s}^{2}}$2${{s}^{2}}$2${{p}^{6}}$, i.e., that of noble gas which is very stable and hence the removal of 2nd electron from ${{Na}^{+}}$ is very difficult. In the case of Mg, after the loss of first electron, electronic configuration of ${{Mg}^{+}}$ ions is 1${{s}^{2}}$2${{s}^{2}}$2${{p}^{6}}$,3${{s}^{1}}$. The second electron to be removed is from 3s orbital which is easier.Hence I${{E}_{2}}$ of sodium is much larger thanI${{E}_{2}}$ of Mg.